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Yet another circle!

Source: INMO 1998 Problem 1

October 6, 2005
geometryindia

Problem Statement

In a circle C1C_1 with centre OO, let ABAB be a chord that is not a diameter. Let MM be the midpoint of this chord ABAB. Take a point TT on the circle C2C_2 with OMOM as diameter. Let the tangent to C2C_2 at TT meet C1C_1 at PP. Show that PA2+PB2=4⋅PT2PA^2 + PB^2 = 4 \cdot PT^2.
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